First off, from what I understand, Facebook will rarely use an image from a root-level URL. For example, if you put http://youtube.com in a Facebook status, you won't see a preview image. Paste the link from an individual video page, you'll see the preview.
Second, Facebook will only use standard image files (.jpg, .png, etc) to create a preview image, it won't create something from a video clip. But wait, you say, when I posted a link to a YouTube video, I see a preview image. If you go to a YouTube video page, and view the source, you will see a line that looks something like this:
<meta property="og:image" content="https://i1.ytimg.com/vi/rKCvhA0xWss/hqdefault.jpg?feature=og">
If you take a look at that .jpg file, you'll see that it's the same thumbnail that appears if you paste the link to the YouTube video in your FB status. All of those meta properties which begin with og stands for the Open Graph Protocol and it's what Facebook uses to determine what your site is about.
So, you'll have to create an image that represents the page, maybe a capture of the video clip. Then you'll have to add the Open Graph Protocol information to your post or page header. If you search the WordPress Plugins Directory for open graph protocol, you'll be able to find plugins that will help you.